Chapter 5 Signals and Noise 1 1 What
![Chapter 5 Signals and Noise 1. 1 What is Noise? any ‘unwanted” part of Chapter 5 Signals and Noise 1. 1 What is Noise? any ‘unwanted” part of](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-1.jpg)
![2 Sources of Instrumental Noise (characterized by their frequency) 2. 1 White Noise – 2 Sources of Instrumental Noise (characterized by their frequency) 2. 1 White Noise –](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-2.jpg)
![Shot Noise -current fluctuations due to random motion of electrons cross a junction (e. Shot Noise -current fluctuations due to random motion of electrons cross a junction (e.](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-3.jpg)
![2. 2 Flicker Noise – amplitude varies with 1/f, drift in instruments 2. 2 Flicker Noise – amplitude varies with 1/f, drift in instruments](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-4.jpg)
![2. 3 Environmental Noise - different forms of noise that arise from the surroundings 2. 3 Environmental Noise - different forms of noise that arise from the surroundings](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-5.jpg)
![2. 4 Composite. Noise Spectrum 2. 4 Composite Spectrum Fig. 5 -3 (p. 113) 2. 4 Composite. Noise Spectrum 2. 4 Composite Spectrum Fig. 5 -3 (p. 113)](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-6.jpg)
![3 Ø Ø Ø Strategies for S/N Enhancement White Noise reduce f, temp, resistance, 3 Ø Ø Ø Strategies for S/N Enhancement White Noise reduce f, temp, resistance,](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-7.jpg)
![3. 1 Reducing f (white noise) 3. 1. 1 Analog filtering: low-pass RC circuit 3. 1 Reducing f (white noise) 3. 1. 1 Analog filtering: low-pass RC circuit](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-8.jpg)
![3. 1. 2 Digital filtering: Fourier transform/smooth control in the frequency domain by manipulating 3. 1. 2 Digital filtering: Fourier transform/smooth control in the frequency domain by manipulating](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-9.jpg)
![3. 2 Increasing f (flicker noise) l l We need to move f to 3. 2 Increasing f (flicker noise) l l We need to move f to](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-10.jpg)
![Lock-in Amplifier Chopper 1. Modulate 2. Amplify modulated signal Fig. 5 -8 (p. 117) Lock-in Amplifier Chopper 1. Modulate 2. Amplify modulated signal Fig. 5 -8 (p. 117)](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-11.jpg)
![3. 3 Signal Averaging l Total intensity of signal: increase linearly with the number 3. 3 Signal Averaging l Total intensity of signal: increase linearly with the number](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-12.jpg)
![3. 3. 1 An Example for Signal Averaging 3. 3. 1 An Example for Signal Averaging](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-13.jpg)
![3. 3. 2 Signal Averaging For a Spectrum Get S/N increased with n½ Need 3. 3. 2 Signal Averaging For a Spectrum Get S/N increased with n½ Need](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-14.jpg)
![3. 3. 3 Boxcar Averaging l A approach for smoothing irregularities l A single 3. 3. 3 Boxcar Averaging l A approach for smoothing irregularities l A single](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-15.jpg)
![3. 3. 3 Boxcar Averaging select a single delay time integrated signal over selected 3. 3. 3 Boxcar Averaging select a single delay time integrated signal over selected](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-16.jpg)
- Slides: 16
![Chapter 5 Signals and Noise 1 1 What is Noise any unwanted part of Chapter 5 Signals and Noise 1. 1 What is Noise? any ‘unwanted” part of](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-1.jpg)
Chapter 5 Signals and Noise 1. 1 What is Noise? any ‘unwanted” part of the analytical signal always some noise in a signal 1. 2 Signal-to-noise ratio (S/N) for a set of data (replicate measurements) for a temporal-varying signal S For meaningful measurements, S/N 3,
![2 Sources of Instrumental Noise characterized by their frequency 2 1 White Noise 2 Sources of Instrumental Noise (characterized by their frequency) 2. 1 White Noise –](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-2.jpg)
2 Sources of Instrumental Noise (characterized by their frequency) 2. 1 White Noise – amplitude invariant with respect to frequency Thermal Noise -voltage fluctuation due to random electron motions in the resistive elements k: Boltzmann’s constant T: absolute temperature R: resistance f: frequency bandwidth,
![Shot Noise current fluctuations due to random motion of electrons cross a junction e Shot Noise -current fluctuations due to random motion of electrons cross a junction (e.](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-3.jpg)
Shot Noise -current fluctuations due to random motion of electrons cross a junction (e. g. , PN interface, space between anode/cathode) I: average current e: charge of electron
![2 2 Flicker Noise amplitude varies with 1f drift in instruments 2. 2 Flicker Noise – amplitude varies with 1/f, drift in instruments](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-4.jpg)
2. 2 Flicker Noise – amplitude varies with 1/f, drift in instruments
![2 3 Environmental Noise different forms of noise that arise from the surroundings 2. 3 Environmental Noise - different forms of noise that arise from the surroundings](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-5.jpg)
2. 3 Environmental Noise - different forms of noise that arise from the surroundings - some occurs at known discrete frequencies - some unpredictable, and difficult to correct (e. g. , TV stations, computers, motors, etc)
![2 4 Composite Noise Spectrum 2 4 Composite Spectrum Fig 5 3 p 113 2. 4 Composite. Noise Spectrum 2. 4 Composite Spectrum Fig. 5 -3 (p. 113)](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-6.jpg)
2. 4 Composite. Noise Spectrum 2. 4 Composite Spectrum Fig. 5 -3 (p. 113)
![3 Ø Ø Ø Strategies for SN Enhancement White Noise reduce f temp resistance 3 Ø Ø Ø Strategies for S/N Enhancement White Noise reduce f, temp, resistance,](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-7.jpg)
3 Ø Ø Ø Strategies for S/N Enhancement White Noise reduce f, temp, resistance, and I Flicker Noise make measurements at frequencies >100 k. Hz Shielding & Grounding absorbing electromagnetic noise But signal § often at or near dc (low freq) § often directly proportional to resistance § often directly proportional to current § often measured with transducers having very large f (fast response, PMT f >107 Hz)
![3 1 Reducing f white noise 3 1 1 Analog filtering lowpass RC circuit 3. 1 Reducing f (white noise) 3. 1. 1 Analog filtering: low-pass RC circuit](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-8.jpg)
3. 1 Reducing f (white noise) 3. 1. 1 Analog filtering: low-pass RC circuit A slow varying dc signal containing high frequencies with bandwidth extending over wide range Fig. 5 -5 (p. 115) High-frequency components rejected, and f reduced
![3 1 2 Digital filtering Fourier transformsmooth control in the frequency domain by manipulating 3. 1. 2 Digital filtering: Fourier transform/smooth control in the frequency domain by manipulating](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-9.jpg)
3. 1. 2 Digital filtering: Fourier transform/smooth control in the frequency domain by manipulating pass function Fig. 5 -12 (p. 121) -It is easy to smooth/filter signal as well as noise. Make sure that the result is not distorted - trade-off between resolution and noise. Need high point density to prevent losing information.
![3 2 Increasing f flicker noise l l We need to move f to 3. 2 Increasing f (flicker noise) l l We need to move f to](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-10.jpg)
3. 2 Increasing f (flicker noise) l l We need to move f to >100 k. Hz… How? - Modulate: encode analytical signal at a high frequency, where 1/f noise is negligible - Amplify the signal at the modulation frequency, while reduce the noise. - demodulate the signal
![Lockin Amplifier Chopper 1 Modulate 2 Amplify modulated signal Fig 5 8 p 117 Lock-in Amplifier Chopper 1. Modulate 2. Amplify modulated signal Fig. 5 -8 (p. 117)](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-11.jpg)
Lock-in Amplifier Chopper 1. Modulate 2. Amplify modulated signal Fig. 5 -8 (p. 117) 3. Demodulate
![3 3 Signal Averaging l Total intensity of signal increase linearly with the number 3. 3 Signal Averaging l Total intensity of signal: increase linearly with the number](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-12.jpg)
3. 3 Signal Averaging l Total intensity of signal: increase linearly with the number (n) of replicate signals l Noise: increase as (n)1/2 à S/N increase as (n)1/2
![3 3 1 An Example for Signal Averaging 3. 3. 1 An Example for Signal Averaging](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-13.jpg)
3. 3. 1 An Example for Signal Averaging
![3 3 2 Signal Averaging For a Spectrum Get SN increased with n½ Need 3. 3. 2 Signal Averaging For a Spectrum Get S/N increased with n½ Need](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-14.jpg)
3. 3. 2 Signal Averaging For a Spectrum Get S/N increased with n½ Need good synchronization for replicate scan Fig. 5 -10 (p. 119)
![3 3 3 Boxcar Averaging l A approach for smoothing irregularities l A single 3. 3. 3 Boxcar Averaging l A approach for smoothing irregularities l A single](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-15.jpg)
3. 3. 3 Boxcar Averaging l A approach for smoothing irregularities l A single –channel signal averager select a single delay time integrated signal over selected gate time average signal for n-replicate repeat at new delay time S/N increases with (averaging time)1/2 Fig. 5 -11 (p. 119)
![3 3 3 Boxcar Averaging select a single delay time integrated signal over selected 3. 3. 3 Boxcar Averaging select a single delay time integrated signal over selected](https://slidetodoc.com/presentation_image/56d002474f7d79f77b082baa3e1ae12f/image-16.jpg)
3. 3. 3 Boxcar Averaging select a single delay time integrated signal over selected gate time average signal for n-replicate repeat at new delay time Fig. 5 -11 (p. 119)
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